Bypass transition mechanism in a rough wall channel flow

The combined effect of wall pulsed jets and roughness in a laminar channel flow is investigated to determine whether or not turbulence can be triggered and maintained at low Reynolds numbers. The study is carried out through a direct numerical simulation based on the lattice Boltzmann method. The roughness, mounted on both walls of the channel, consists of transverse square bars spanning the whole width of the channel. Rectangular orifice(s) at the bottom wall act as pulsed jets. The jets are pulsed only once with the second jet activated at the end of the cycle of the first jet. Without activating the jets, the flow in the rough wall channel consists mainly in steady secondary motions in the canopies (spaces between bars) and a skimming two-dimensional laminar flow with some oscillations above the canopies. When the jets are activated, a localized three-dimensional turbulence develops and grows in the channel. Not only it is found that this localized turbulence bears strong similarity to that of a fully rough wall turbulent channel flow, but it appears to be in a “pseudo-” fully rough regime, as observed by the relatively negligible (averaged) viscous drag as compared to the form drag generated by the roughness elements. The physical mechanism which allows this to occur is discussed.

Figure 1

Schematic of configuration of the channel (a short segment between the domain $0\le x/h\le 5$). The jets are mounted only at the bottom wall (at $x/h=1.09$) where two parallel plates are roughened by 2D square bars.

Figure 2

Flow visualization-based ${\lambda }_2$ contour $\left(\frac{{\lambda }_2}{{\lambda }_{2,\max }}=-0.01\right)$ at $t^{*}=0.5$ on a rough wall, shortly after the jet(s) have complete their blowing cycle. The first orifice is placed behind the second orifice, which is shifted in the spanwise direction.

Figure 3

Flow visualizations based on ${\lambda }_2$ contour $\left(\frac{{\lambda }_2}{{\lambda }_{2,\max }}=-0.01\right)$ over the pulsating rough wall at (a) $t^{*}=3.5$, (b) $t^{*}=5.5$, (c) $t^{*}=6.6$.

Figure 4

Isocontours of ${\omega }_z$ at $t^{*}=4.4$. (a) Rough wall without pulsing, (b) rough wall with pulsing; $2.5\le x/h\le 5$.

Figure 5

Isocontours of ${\omega }_z$ at $t^{*}=5.5$. (a) Rough wall without pulsing, (b) rough wall with pulsing; $2.5\le x/h\le 5$.

Figure 6

Mean velocity streamlines in the ($x,y$) plane (averaged along $z$). $t^{*}=37.5$: (a) rough wall, (b) rough wall with pulsing; $t^{*}=65.5$: (e) rough wall, (f) rough wall with pulsing. Vector fields of the velocity fluctuations in the ($x,y$) plane (averaged along $z$). $t*=37.5$: (c) rough wall, (d) rough wall with pulsing; $t^{*}=65.5$: (g) rough wall, (h) rough wall with pulsing.

Figure 7

${\lambda }_2$ contour $\left(\frac{{\lambda }_2}{{\lambda }_{2,\max }}=-0.01\right)$ at (a) $t^{*}=28.0$, (b) $t^{*}=32$, and (c) $t^{*}=42$. The region shown corresponds to $7.5\le x/h\le 12.5$.

Figure 8

Visualization of the localized turbulence at $t^{*}=42$ based on ${\lambda }_2$ criteria.

Figure 9

Time variation of the averaged kinetic energy $E$ for the rough wall with two pulsing ($——$), without pulsing (- - - - -). Inset: early stage of during and after jets in between $0\le t^{*}\le 0.9$.

Figure 10

Normalized mean velocity profiles for the limited spatial averaging at $t^{*}=42$ for a rough wall: without pulsing ($•$) and two pulsing ($——$: upper half), ($-\; -\; -\; -\; -$: lower half). DNS of a fully developed turbulent rough channel flow [5] (open symbols). Inset: Double (time and space) averaged; $-\; -\; -\; -\; -$: smooth wall with jets; $-•-$: smooth wall without jets.

Figure 11

Distributions of the velocity rms $u_i^{\prime +}$ at $t^{*}=42$ on the rough wall: (a) without jet ($u_1^{\prime }$: $-\; -\; -\; -$; $u_2^{\prime }$: $-\; -\; -\; -$; $u_3^{\prime }$: $——$); (b) with two jets ($u_1^{\prime }$: $——$, $u_2^{\prime }$: $——$, $u_3^{\prime }$: $——$).

Figure 12

Nondimensionalized root mean square (rms) velocity fluctuations (a, b, c) and Reynolds shear stress (d) distributions on a rough wall with two jets at $t^{*}=42$ (closed symbols) compared to the DNS at a similar Reynolds number of a fully developed rough channel [5] (open symbols) (see the text for details).

Figure 13

Time variation of the averaged kinetic energy $E$ for a rough wall with jets at $t^{*}=30$ (pulsating at $t^{*}=0$: $——$; pulsating at $t^{*}=30$: $——$; without jets: $——$).

Figure 14

Distributions of nondimensionalized rms velocity fluctuations on a rough wall with two jets activated at $t^{*}=0$ ($t^{*}=42$, closed circles) and at $t^{*}=30$ ($t^{*}=76$, closed triangles).

Figure 15

Flow visualization based ${\lambda }_2$ contour $\left(\frac{{\lambda }_2}{{\lambda }_{2,\max }}=-0.01\right)$ at $t^{*}=42$ on the rough wall: (a) one jet, (b) two jets. The region shown corresponds to $8.1\le x/h\le 17.5$; the section $x/h=17.5$ is the channel outlet.

Figure 16

Distributions of the velocity rms $u_i^{\prime +}$: one jet ($u^{\prime +}$: $-○-$, $w^{\prime +}$: $-▵-$), two jets ($u^{\prime +}$: $-•-$, $w^{\prime +}$: $-▴-$) at $t*=42$.